The performance of audio source separation from underde- termined convolutive mixture assuming known mixing filters can be significantly improved by using an analysis sparse prior optimized by a reweighting l1 scheme and a wideband data- fidelity term, as demonstrated by a recent article. In this letter, we show that the performance can be improved even more significantly by exploiting a low-rank prior on the source spectrograms. We present a new algorithm to estimate the sources based on i) an analysis sparse prior, ii) a reweighting scheme so as to increase the sparsity, iii) a wideband data-fidelity term in a constrained form, and iv) a low-rank constraint on the source spectrograms. Evaluation on reverberant music mixtures shows that the resulting algorithm improves state-of-the-art methods by more than 2 dB of signal-to-distortion ratio.